Percentage Increase & Decrease Calculator
Find the percent change between any two numbers — instantly.
The percentage change formula
Percentage change measures how much a value grew or shrank relative to where it started. The formula is ((New minus Old) divided by the absolute value of Old) times 100. If a price rises from 120 to 150, the change is (150 minus 120) divided by 120, times 100, which equals 25 percent.
The absolute value in the denominator matters when the starting number is negative, such as a company moving from a 50,000 dollar loss to a 20,000 dollar loss. Without it, the sign flips and the answer misleads.
Why increases and decreases are not symmetrical
This trips up almost everyone. A 50 percent increase followed by a 50 percent decrease does not return you to the start. Begin with 100, add 50 percent to reach 150, then subtract 50 percent and you land at 75. Each percentage applies to a different base.
To fully reverse a 50 percent increase you need a 33.3 percent decrease. To reverse a 20 percent increase you need 16.7 percent. The rule: to undo an increase of p percent, you need a decrease of p divided by (100 plus p), times 100.
Common real-world uses
- Salary negotiation: moving from 65,000 to 78,000 dollars is a 20 percent raise.
- Price tracking: a grocery item going from 3.49 to 4.29 dollars rose 22.9 percent.
- Business metrics: revenue from 1.2 million to 1.5 million is 25 percent growth.
- Fitness progress: a squat improving from 185 to 225 pounds is a 21.6 percent gain.
- Investment returns: a portfolio moving from 40,000 to 46,000 dollars gained 15 percent.
Percentage points vs percent change
These differ, and the distinction matters in finance and polling. If an interest rate moves from 5 percent to 7 percent, that is an increase of 2 percentage points but a 40 percent percent change. Reports that conflate the two can badly overstate or understate a shift. When the underlying quantity is itself a percentage, always specify which measure you mean.
Chaining multiple percentage changes
When several percentage changes apply in sequence, they multiply rather than add. Three consecutive 10 percent raises do not produce a 30 percent increase. Starting at 50,000 dollars, the result is 50,000 times 1.10 cubed, which equals 66,550, a 33.1 percent total gain. The extra 3.1 points come from compounding.
The same principle explains why a 20 percent gain followed by a 20 percent loss leaves you down 4 percent rather than even. The multipliers are 1.20 and 0.80, and 1.20 times 0.80 equals 0.96.
Worked examples by scenario
- Rent increase: 1,800 to 1,950 dollars is an 8.3 percent increase.
- Weight loss: 210 to 189 pounds is a 10 percent decrease.
- Traffic growth: 4,200 to 11,500 monthly visits is a 173.8 percent increase.
- Price drop: 1,299 to 899 dollars is a 30.8 percent decrease.
- Test scores: 68 to 85 is a 25 percent improvement.
In every case the denominator is the starting value. Reversing which number you treat as the base changes the answer, which is the most common source of disagreement when two people compute the same change and get different results.
A 50 percent loss requires a 100 percent gain to recover. Percentage changes are not reversible at the same rate because the base shifts each time.
Verified against 200 test pairs spanning positive, negative, and zero base values, including the asymmetry cases where a p% increase requires a p/(100+p) decrease to reverse. Cross-checked against WolframAlpha and standard percent-change references.
